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Abstract
Methods of polynomial degree d to approximate integrals over the surface of the s-dimensional sphere are discussed. Such methods are constructed by choosing the abscissas and weights so that the formulas integrate a certain subset of the polynomials of maximum degree d, exactly. A simple set of monomials is described, the exact integration of which will ensure that the method has the required polynomial degree. Results are obtained which enable the derivation of consistency conditions on the rule structures. An example of a new s-dimensional degree-11 rule is given.
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